A Statistical Framework for Analyzing Specification Resistance to Learnware-Inversion Risks

The learnware paradigm enables model reuse by pairing each submitted model with a specification, a public artifact used to identify helpful models without raw-data exchange. This design creates a privacy surface: a useful specification must reveal capability-relevant information, but such information should not expose sensitive properties of training data or user tasks. Is it achievable in practice? To answer this question, this paper establishes the first framework for analyzing the incremental risk introduced by specifications in learnware, and provides theoretical guarantees for the widely used reduced kernel mean embedding (RKME) specification. Specifically, we formulate learnware-inversion as a family of statistical decision games and define the risk of specification as the incremental Bayes value from observing the model alone to observing the complete learnware. For the RKME specification, we derive risk bounds through an RKHS-smoothed total-variation bridge and the stability analysis of its reduced-set generator. We further instantiate the framework for common attacks and show that a properly sized RKME specification introduces negligible additional privacy risk while retaining sufficient information for learnware identification.